Consider a vessel filled with a liquid up to height $H$. The bottom of the vessel lies in the X-Y plane passing through the origin. The density of the liquid varies with Z-axis as $\rho(z) = \rho_0 \left[2 - (z/H)^2\right]$. If $P_1$ and $P_2$ are the pressures at the bottom surface and top surface of the liquid, the magnitude of $(P_1 - P_2)$ is: